Influence of inhomogeneous temperature and field distribution on sound generation and its effect on reflectivity of a thin film heated by a femtosecond pulse

Abstract

One of the main methods for obtaining information about the generation of sound pulses in metals is to measure the reflection coefficient of a probe wave. Various theoretical models are used to interpret the results of measuring the contribution to reflection coefficient ΔR(t) due to sound-generated displacements of lattice atoms. The purpose of this paper is to establish the degree of accuracy of models used in the case of sound generation in thin films exposed to a femtosecond pulse. It is shown below that the assumption of uniform heating used for thin films is justified if the film thickness is less than the film heating depth and for thicker films at times greater than the film heating time over the entire thickness. For optically thick films, a relatively simple expression for the field can be used. If the film thickness is less than the skin layer depth of the pump field, then it is necessary to consider the field reflection from a substrate. In this case, depending on the optical properties of the metal and the substrate, taking into account reflection can lead to either an increase or a decrease in ΔR(t). It has been established that if the skin layer at the frequency of probe radiation is less than the film heating depth, then taking into account temperature gradients in the equation for the displacement of lattice atoms leads to small changes in ΔR(t). This makes it possible to significantly simplify calculations of the displacement of lattice atoms.